Least squares methods in maximum likelihood problems
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The Gauss-Newton algorithm for solving nonlinear least squares problems proves particularly efficient for solving parameter estimation problems when the number of independent observations is large and the fitted model is appropriate. In this context the conventional assumption that the residuals are small is not needed. The Gauss-Newton method is a special case of the Fisher scoring algorithm for maximizing log likelihoods and shares with this a number of desirable properties. The formal...[Show more]
dc.contributor.author | Osborne, Michael | |
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dc.date.accessioned | 2015-12-07T22:50:39Z | |
dc.identifier.issn | 1055-6788 | |
dc.identifier.uri | http://hdl.handle.net/1885/27107 | |
dc.description.abstract | The Gauss-Newton algorithm for solving nonlinear least squares problems proves particularly efficient for solving parameter estimation problems when the number of independent observations is large and the fitted model is appropriate. In this context the conventional assumption that the residuals are small is not needed. The Gauss-Newton method is a special case of the Fisher scoring algorithm for maximizing log likelihoods and shares with this a number of desirable properties. The formal structural correspondence is striking with the linear subproblem for the general scoring algorithm having the form of a linear least squares problem. This is an important observation because it provides likelihood methods with a computational framework, which accords with computational orthodoxy. Both line search and trust region algorithms are available and these are compared and contrasted here. It is shown that the types of theoretical results that have led to the wide acceptance of trust region methods have direct equivalents in the line search case, while the latter have better transformation invariance properties. Computational experiments for both continuous and discrete distributions show no advantage for the trust region approach. | |
dc.publisher | Taylor & Francis Group | |
dc.source | Optimization Methods and Software | |
dc.subject | Keywords: Fisher scoring; Gauss-Newton method; Least squares formulation; Line search implementation; Numerical comparisons; Trust region implementation; Algorithms; Maximum likelihood estimation; Optimization; Parameter estimation; Problem solving; Least squares a Fisher scoring; Gauss-Newton method; Least squares formulation; Line search implementation; Numerical comparisons; Trust region implementation | |
dc.title | Least squares methods in maximum likelihood problems | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 21 | |
dc.date.issued | 2006 | |
local.identifier.absfor | 010399 - Numerical and Computational Mathematics not elsewhere classified | |
local.identifier.ariespublication | u3488905xPUB49 | |
local.type.status | Published Version | |
local.contributor.affiliation | Osborne, Michael, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 6 | |
local.bibliographicCitation.startpage | 943 | |
local.bibliographicCitation.lastpage | 959 | |
local.identifier.doi | 10.1080/10556780600874154 | |
dc.date.updated | 2015-12-07T12:19:41Z | |
local.identifier.scopusID | 2-s2.0-33748855833 | |
Collections | ANU Research Publications |
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